Debutant Adam Curry and leading goalscorer Kabongo Tshimanga struck inside the final 12 minutes to pull United back from the brink of elimination.
Andre Brown and Joe Ironside had earlier put the slick Harriers in control but United responded impressively under new manager Craig Elliott to force a replay on Tuesday.
Hull City loanee Curry was handed his debut at left-back, while Derby County youngster Kyron Stabana appeared on the opposite side of defence.
The loan players — and United as whole — found themselves under the cosh in the first half and Harriers spurned eight presentable openings before the break.
George Willis denied Brown, Elton Ngwatala headed wide from James Pearson’s deep cross and Ironside lifted an effort too high as Harriers started like an express train.
Ironside, Ngwatala and Brown each had further chances, while Ryan Croasdale fizzed an effort off target from distance and Declan Weeks was only denied by a terrific Jamie McGuire clearance on the goalline.
Harriers finally went in front 11 minutes after half-time when Croasdale teed up Pearson to cross from the right and once Ironside had nodded the ball down, BROWN finished expertly on the turn.
It was seemingly game, set and match 10 minutes later when James McQuilkin’s deep corner was guided home by the head of IRONSIDE but United ultimately had other ideas.
Two long-range bullets from McGuire set the tone for United and from a resulting Ashley Hemmings corner, CURRY curled home a fine left-footed effort on his United debut.
The comeback was completed two minutes later when Hemmings again turned provider to afford TSHIMANGA a tap-in at the back post.
Hemmings almost assumed the role of match-winner with five minutes to play but his fierce drive was spectacularly tipped to safety by visiting keeper Brandon Hall.
Boston (4-3-3): George Willis; Kyron Stabana, Brad McGowan, Brad Beatson, Adam Curry; Jordan Keane, Jamie McGuire, Harry Vince (Jay Rollins 63); James Clifton (Kabongo Tshimanga 63), Reece Thompson, Ashley Hemmings. Subs (not used): Jan Yeomans, Gregg Smith, Jack Broadhead.
Kidderminster (4-2-3-1): Brandon Hall; James Pearson, James O'Connor, Fraser Horsfall, Sam Austin; Ryan Croasdale, James McQuilkin; Declan Weeks, Andre Brown (Emmanuel Sonupe 67), Elton Ngwatala; Joe Ironside. Subs (not used): Yan Klukowski, Gabriel Danko, Dale Eve (gk).
Referee: Declan Bourne.
Attendance: 732 (58 visitors).